Burnel has been a member of the Stranglers since the group's inception in 1974, but has also made two solo albums: Euroman Cometh in 1979, and Un Jour Parfait in 1988, as well as a collaborative album with fellow Stranglers member Dave Greenfield, Fire and Water (Ecoutez Vos Murs) in 1983.[4] Burnel has also produced and appeared as a guest musician for a number of artists, such as Lizard and ARB from Japan, Polyphonic Size (from Belgium) and Taxi Girl's album, Seppuku, in 1981, as well as Laurent Sinclair's "Devant le Miroir" maxi single. Burnel also formed a rhythm and blues covers band, the Purple Helmets, who played a number of concerts and released two albums in the late 1980s.

As a French citizen, Burnel received his call-up papers for national service in France. He succeeded in avoiding it with a novel defence, arguing that his absence would indirectly damage the Stranglers as a band, and therefore the careers of the other members. This was in accordance with Burnel's claim that only the "bourgeois" would ever agree to serve their country's military.

Burnel is noted for his distinctive bass guitar sound and melodic bass lines. These are particularly prominent on earlier Stranglers recordings produced by Martin Rushent, such as the hit singles "No More Heroes" and "Peaches". In the early days, Burnel's distinctive aggressive sound was created using a Fender Precision Bass with RotoSound roundwound strings played with a plectrum very close to the bridge, through Hiwatt all-valve amplification,[5] however the defining factor was the use of a Marshall 4x12 speaker cabinet in which the speaker cones were ripped, creating a distorted sound.[6] Later, he used a Yamaha BB2000, a Steinberger L2 (headless), and a Kinkade acoustic bass. He currently plays Shuker JJ Burnel signature basses custom-built in England by Jon Shuker. He was one of the first bass guitarists to use Trace Elliot amplification when the company began production in 1980. He now uses amplification by Ashdown Engineering who have honoured him with his own JJ500 signature amps. Burnel has been a RotoSound endorser since the early 1980s, and has featured in their advertising.

Burnel is a black belt 7th dan (nanadan), karate expert,[7] and is head of Shidokan UK.[8] He once used these skills to assault rock journalist Jon Savage after a mildly critical review. Savage was left with facial injuries. He is also a motorcyclist and has owned many Triumph motorbikes.[9]